On the convergence of greedy algorithms for initial segments of the Haar basis
Functional Analysis
2015-05-13 v1
Abstract
We consider the -Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in () then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.
Keywords
Cite
@article{arxiv.0905.3036,
title = {On the convergence of greedy algorithms for initial segments of the Haar basis},
author = {S. J. Dilworth and E. Odell and Th. Schlumprecht and A. Zsak},
journal= {arXiv preprint arXiv:0905.3036},
year = {2015}
}